Yamlalias: Rotation, Translation, Rotations, Translations, Scale, Flip, Affine
If we want to rotate, we can add one single scalar. We can do that by using this transformation matrix, and justby using a single number we can rotate.
This preserves angles and distances.
Of course you remember that each column of the transform where the unit vectors are gonna land.
Then, with
For
In fact, when
If you transpose an orthogonal matrix(rotation), you get its inverse matrix, which is the exact rotation but backwards.
So with
Now we add a scaling factor to the two axes.
Preserve angles and ratio between distances.
Because as you remember, the unit vectors have two components,
The main component of
Here we are just scaling the main components of the two vectors.
We add
Preserve preserve parallelism but not angles.
There are two ways to shear:
Since in this case we have only 1 angle, we are using the second way. The shear can only happen if we rotate the vectors, since if the secondary component is 0 in both of the basis vectors, unless it is rotated.
So, here, the C coefficients serve the purpose of scaling the secondary component of the unit vectors, which is rotated.